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Math Camp 1: Functional analysis

Math Camp 1: Functional analysisAbout the primerGoalTo briefly review concepts in Functional analysis thatwill be used throughout the course. The followingconcepts will be described1. Function spaces2. Metric spaces3. Dense subsets4. Linear spaces5. Linear functionals The definitions and concepts come primarily from Introductory RealAnalysis by Kolmogorov and Fomin (highly recommended).6. Norms and semi-norms of linear spaces7. Euclidean spaces8. Orthogonality and bases9. Separable spaces10. Complete metric spaces11. Hilbert spaces12. Riesz representation theorem13. Convex functions14. Lagrange multipliersFunction spaceAfunction spaceis a space made of functions.

4. The set of all probability densities with Kullback-Leibler divergence ρ(p1(x),p2(x)) = Z ln p1(x) p2(x) p1(x)dx is not a metric space. The divergence is …

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